Analytical formulation for exciton in semiconductor quantum dot with parabolic confinement

The exciton properties in cubical quantum dot (CQD), with parabolic confining potential, are theoretically investigated. We have used the twoband model, the effective mass approximation, and the variational method. The analytical expressions of the binding energy, the normalized photoluminescence energy transition, the spatial extension, and the oscillator strength of the exciton, in the ground state, have been obtained. The numerical calculations for the typical GaAs/Al_xGa_1-xAs CQD are presented. The effects of the cubic quantum dot length and the Al-concentration on the exciton properties are discussed. The results of the calculation illuminate that Al-concentration and the CQD length can make an important impact on the exciton binding energy and the photoluminescence peak energy.